I wasn't allowed to watch TV as a kid, so my references are definitely lacking. This is a running list - add your own suggestions below!
  1. Adventures in Babysitting
  2. Finding Nemo
    Assuming the mobile phone was waterproof and you got decent subsea reception.
  3. Pretty much any film based on a Shakespeare storyline.
    Except maybe 10 Things I Hate About You.
  4. The Princess Bride
    Wesley could have just called, right?
  5. Heathers
    Ok, not the whole plot. But Veronica could have googled what "ich lüge" bullets actually were.
  6. Phone Booth
    Colin Farrell could've just left that booth
    Suggested by @pokeymouth